Spin-Peierls Instability of Three-Dimensional Spin Liquids with Majorana Fermi Surfaces

TL;DR

This paper explores how three-dimensional Kitaev spin liquids with Majorana Fermi surfaces become unstable due to additional interactions, leading to a spin-Peierls transition that doubles the unit cell and forms a spin liquid with line nodes.

Contribution

It demonstrates that Majorana Fermi surfaces in 3D Kitaev models are inherently unstable to spin-Peierls instabilities caused by generic interactions.

Findings

Majorana Fermi surfaces are always unstable under additional interactions.

The system spontaneously doubles its unit cell at very low temperatures.

The resulting phase features line nodes and possible symmetry breaking.

Abstract

Three-dimensional (3D) variants of the Kitaev model can harbor gapless spin liquids with a Majorana Fermi surface on certain tricoordinated lattice structures such as the recently introduced hyperoctagon lattice. Here we investigate Fermi surface instabilities arising from additional spin exchange terms (such as a Heisenberg coupling) which introduce interactions between the emergent Majorana fermion degrees of freedom. We show that independent of the sign and structure of the interactions, the Majorana surface is always unstable. Generically the system spontaneously doubles its unit cell at exponentially small temperatures and forms a spin liquid with line nodes. Depending on the microscopics further symmetries of the system can be broken at this transition. These spin-Peierls instabilities of a 3D spin liquid are closely related to BCS instabilities of fermions.